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    1 TitleText('Calculus: Early Transcendentals') 
    2 EditionText('1')
    3 AuthorText('Rogawski')
    4 
    5 1 >>> Precalculus Review
    6 1.1 >>> Real Numbers, Functions, and Graphs
    7 1.2 >>> Linear and Quadratic Functions
    8 1.3 >>> The Basic Classes of Functions
    9 1.4 >>> Trigonometric Functions
   10 1.5 >>> Inverse Functions
   11 1.6 >>> Exponential and Logarithmic Functions
   12 1.7 >>> Technology: Calculators and Computers
   13 2 >>> Limits
   14 2.1 >>> Limits, Rates of Change, and Tangent Lines
   15 2.2 >>> Limits: A Numerical and Graphical Approach
   16 2.3 >>> Basic Limit Laws
   17 2.4 >>> Limits and Continuity
   18 2.5 >>> Evaluating Limits Algebraically
   19 2.6 >>> Trigonometric Limits
   20 2.7 >>> Intermediate Value Theorem
   21 2.8 >>> The Formal Definition of a Limit
   22 3 >>> Differentiation
   23 3.1 >>> Definition of the Derivative
   24 3.2 >>> The Derivative as a Function
   25 3.3 >>> Product and Quotient Rules
   26 3.4 >>> Rates of Change
   27 3.5 >>> Higher Derivatives
   28 3.6 >>> Trigonometric Functions
   29 3.7 >>> The Chain Rule
   30 3.8 >>> Implicit Differentiation
   31 3.9 >>> Derivatives of Inverse Functions
   32 3.10 >>> Derivatives of General Exponential and Logarithmic Functions
   33 3.11 >>> Related Rates
   34 4 >>> Applications of the Derivative
   35 4.1 >>> Linear Approximation and Applications
   36 4.2 >>> Extreme Values
   37 4.3 >>> The Mean Value Theorem and Monotonicity
   38 4.4 >>> The Shape of a Graph
   39 4.5 >>> Graph Sketching and Asymptotes
   40 4.6 >>> Applied Optimization
   41 4.7 >>> L'Hopital's Rule
   42 4.8 >>> Newton's Method
   43 4.9 >>> Antiderivatives
   44 5 >>> The Integral
   45 5.1 >>> Approximating and Computing Area
   46 5.2 >>> The Definite Integral
   47 5.3 >>> The Fundamental Theorem of Calculus, Part I
   48 5.4 >>> The Fundamental Theorem of Calculus, Part II
   49 5.5 >>> Net or Total Change as the Integral of a Rate
   50 5.6 >>> Substitution Method
   51 5.7 >>> Further Transcendental Functions
   52 5.8 >>> Exponential Growth and Decay
   53 6 >>> Applications of the Integral
   54 6.1 >>> Area Between Two Curves
   55 6.2 >>> Setting Up Integrals: Volumes, Density, Average Value
   56 6.3 >>> Volumes of Revolution
   57 6.4 >>> The Method of Cylindrical Shells
   58 6.5 >>> Work and Energy
   59 7 >>> Techniques of Integration
   60 7.1 >>> Numerical Integration
   61 7.2 >>> Integration by Parts
   62 7.3 >>> Trigonometric Integrals
   63 7.4 >>> Trigonometric Substitution
   64 7.5 >>> Integrals of Hyperbolic and Inverse Hyperbolic Functions
   65 7.6 >>> The Method of Partial Fractions
   66 7.7 >>> Improper Integrals
   67 8 >>> Further Applications of the Integral and Taylor Polynomials
   68 8.1 >>> Arc Length and Surface Area
   69 8.2 >>> Fluid Pressure and Force
   70 8.3 >>> Center of Mass
   71 8.4 >>> Taylor Polynomials
   72 9 >>> Introduction to Differential Equations
   73 9.1 >>> Solving Differential Equations
   74 9.2 >>> Models Involving y'=k(y-b)
   75 9.3 >>> Graphical and Numerical Methods
   76 9.4 >>> The Logistic Equation
   77 9.5 >>> First-Order Linear Equations
   78 10 >>> Infinite Series
   79 10.1 >>> Sequences
   80 10.2 >>> Summing an Infinite Series
   81 10.3 >>> Convergence of Series with Positive Terms
   82 10.4 >>> Absolute and Conditional Convergence
   83 10.5 >>> The Ratio and Root Tests
   84 10.6 >>> Power Series
   85 10.7 >>> Taylor Series
   86 11 >>> Parametric Equations, Polar Coordinates, and Conic Sections
   87 11.1 >>> Parametric Equations
   88 11.2 >>> Arc Length and Speed
   89 11.3 >>> Polar Coordinates
   90 11.4 >>> Area and Arc Length in Polar Coordinates
   91 11.5 >>> Conic Sections
   92 12 >>> Vector Geometry
   93 12.1 >>> Vectors in the Plane
   94 12.2 >>> Vectors in Three Dimensions
   95 12.3 >>> Dot Product and the Angle Between Two Vectors
   96 12.4 >>> The Cross Product
   97 12.5 >>> Planes in Three-Space
   98 12.6 >>> A Survey of Quadric Surfaces
   99 12.7 >>> Cylindrical and Spherical Coordinates
  100 13 >>> Calculus of Vector-Valued Functions
  101 13.1 >>> Vector-Valued Functions
  102 13.2 >>> Calculus of Vector-Valued Functions
  103 13.3 >>> Arc Length and Speed
  104 13.4 >>> Curvature
  105 13.5 >>> Motion in Three-Space
  106 13.6 >>> Planetary Motion According to Kepler and Newton
  107 14 >>> Differentiation in Several Variables
  108 14.1 >>> Functions in Two or More Variables
  109 14.2 >>> Limits and Continuity in Several Variables
  110 14.3 >>> Partial Derivatives
  111 14.4 >>> Differentiability, Linear Approximation, and Tangent Planes
  112 14.5 >>> The Gradient and Directional Derivatives
  113 14.6 >>> The Chain Rule
  114 14.7 >>> Optimization in Several Variables
  115 14.8 >>> Lagrange Multipliers: Optimizing with a Constraint
  116 15 >>> Multiple Integration
  117 15.1 >>> Integrals in Several Variables
  118 15.2 >>> Double Integrals over More General Regions
  119 15.3 >>> Triple Integrals
  120 15.4 >>> Integration in Polar, Cylindrical, and Spherical Coordinates
  121 15.5 >>> Change of Variables
  122 16 >>> Line and Surface Integrals
  123 16.1 >>> Vector Fields
  124 16.2 >>> Line Integrals
  125 16.3 >>> Conservative Vector Fields
  126 16.4 >>> Parametrized Surfaces and Surface Integrals
  127 16.5 >>> Integrals of Vector Fields
  128 17 >>> Fundamental Theorems of Vector Analysis
  129 17.1 >>> Green's Theorem
  130 17.2 >>> Stokes' Theorem
  131 17.3 >>> Divergence Theorem